Cross-sectional model for cold neutron scattering in liquid 4He

The dynamics of liquid 4He at all temperature between 1.0 and 4.2 K is described in terms of a double-differential cross-sectional model for cold neutron scattering. The major features of the model are as follows: decomposition into quasiparticle (phonon-roton) and density components weighted with a temperature-dependent fraction of Bose condensation; transition of coherent scattering from a one-phonon Lorentzian peak at small momentum transfer to a Gaussian shape of elastic scattering by a free nucleus at large momentum transfer; and characterization with fundamental parameters such as excitation energy and its intrinsic width for phonon and roton. Satisfactory agreement with experimental cross-sectional results, both double-differential and total, is obtained, which enables us to apply the present model for the quantitative evaluation of ultra- and very-cold neutron production.